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arXiv · 2610.19634

Catalan polynomials for the Wishart-Laguerre $β$-ensemble

Bei Kang·Lu-Yao Wang·Ke Wu·Wei-Zhong Zhao
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Abstract

By means of $W$-representation, we investigate the Wishart-Laguerre $β$-ensemble and present a compact expression for Catalan polynomials. For a special Nekrasov partition function associated with the Wishart-Laguerre $β$-ensemble, we show that it can be expressed as a exponential form of the special Catalan polynomials. Furthermore, we make a rule to calculate the Catalan polynomials by means of Feynman diagrams and present another expression for Catalan polynomials. We also establish the connection between certain Catalan polynomials and knot theory.

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Bei Kang, Lu-Yao Wang, Ke Wu, Wei-Zhong Zhao. 2026-10-14. Catalan polynomials for the Wishart-Laguerre $β$-ensemble. https://arxiv.org/abs/2610.19634

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